I am an orc cleric worshiping Luthic. Can I worship an additional god like Bane or Cyric, any evil ones? Does Luthic allow that? I would like for this character to become a blackguard, if that is possible for a worshiper of Luthic.
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Since this is a bit of a wall of text, the upfront answers to this question are "you can worship two gods, but only get power from one outside of a couple specific circumstances" and "blackguards of Luthic are a-okay."
Moving on, though:
Worship of Two Gods: Maybe
There are a couple important rules regarding this question scattered about in various books. The most notable of which is the cleric description in the Player's Handbook, on page 30:
On page 32:
And, importantly, on page 106:
These three quotes are the core rules on worshipping gods, and together they say the following three things:
There are also rules in Deities and Demigods about worshipping pantheons of deities, on page 6. There are "loose pantheons" (grouped by association with a region or area, rather than being one organization), and "tight pantheons" (groups of gods that are effectively a single unit, even when they clash). The Faerûnian gods are listed as a loose pantheon—generally, a person on Toril will worship one or more of them, sometimes giving prayer to multiples in the same day, but a cleric chooses one to focus on and draw power from. In contrast, the Norse and Greek pantheons are tight pantheons; when a cleric worships them, they have a choice of either choosing a single individual to worship (and choosing from their domains), or worshipping the pantheon as a whole (and choosing any combination of domains possessed by the whole pantheon).
Faerûn's gods and the fact that people often pray to multiples is also outlined in the Forgotten Realms Campaign Setting, on page 232.
The pantheon rules aren't particularly relevant to Luthic and Bane/Cyril, but it's worth noting that there is precedent for worshipping multiple gods. You can definitely worship one god and gain power from them, and pray to a second or third god as you like, but whether or not you can gain abilities from your worship of more than one gods who are not in a tight pantheon is entirely up to your DM.
Alternatively, you could see if your DM would allow you to use this rule:
To allow you to treat your worship of multiple deities as your spiritual inclination. Normally, clerics of an ideal refer to ones who worship no gods, but I think it's perfectly reasonable to adapt the concept to worshipping multiple gods, or even an alternate interpretation of a god (such as the famous Pelor, the Burning Hate).
Regarding the fluff, each of Luthic, Bane, and Cyric are evil. However, it's possible that Bane may be at odds with Cyric, being as they are on opposite ends of the evil spectrum (Lawful Evil vs Chaotic Evil). Luthic is Neutral Evil, however, and it makes sense that a cleric of all three could make their sensibilities fit with that alignment. Another good candidate for sharing cleric brainspace with a worshipper of Luthic is Grumsh. After all, Grumsh and Luthic are a married couple.
Blackguards of Luthic: Yes
The Dungeon Master's Guide's entry for the blackguard class lists no required deity. They list the following as vague power sources:
But it is not a mechanic that comes up in the class. In fact, you can be a blackguard without having anything to do with fiends and evil gods, so long as you meet the aligment requirement and have had friendly contact with an evil outsider at some point. This also means that as long as your god is evil, they're likely to allow you to progress as a blackguard.
Where your blackguard spells and powers come from is up to you and your DM, though. It's perfectly reasonable to say that they're granted by your god(s), but it might also be that they're a dark mirror of the paladin class, who is called to action directly by the concepts of good and law, rather than any specific deity or power.
You may only have one spell-granting god (with the exception of gods are are actually a bunch of dudes, like the Sovereign Host in Eberron).
Page 32, PHB:
There is no option given to the cleric to choose multiple deities, just one or none.
You can certainly attempt to align your agenda with multiple gods, but not receive spells from multiples.
Notably, Blackguards do not have a "deity" section in their DMG entry. They only have a mention of "serving dark deities" but nothing is said about these deities granting spells to the blackguard, or being involved in any way other than being served.